《Causal Calculation Song》 - Inkisanka

Japanese: 《因帰算歌》 - いんきさんか

…Since it was published after Jinkoki, it is more of a commentary on Jinkoki, but it is rich in content and includes problems on Kameiwari, Dando, and Tsukishiochi's posthumous problems. The name of this work means that it corrects errors in mathematics books such as Jinkoki, Imamura Tomoaki's Inkisanka (1640), and Enami Kazuzumi's Sanryoroku (1653). In addition to criticizing Sanryoroku, he solved the problems left behind in Jinkoki and submitted 11 more problems, which spurred the succession of the problems. …

From [Arithmetic]

…In China, the Sun Tzu Suanjing (said to be a book from the Six Dynasties period) shows a pheasant and a rabbit. In Japan, the oldest example seems to be in Imamura Tomoaki's Inki Sanka (1640), which also shows a pheasant and a rabbit. The first examples of a crane and a turtle appear in Sakabe Hirotaka's Sanpo Tenzan Shinanroku (1810). …

From [Tateiroku]

…It can be said that mathematics in the Edo period started with two excellent textbooks, Jinkoki and Tateiroku. The following year, Imamura published Inkisanka, a collection of all mathematical formulas written in poems. Tateiroku was given a detailed commentary by his student Ando Yuasa and published under the title Tateiroku Kana-sho (1662). …

From 【Wasan】

...It also includes Imamura's own ideas. The following year, Imamura published a collection of formulas in the form of tanka, Inkisanka (1640), to meet the needs of beginners. In 1641, Yoshida published a small three-volume version of Jinkoki, which was edited differently from the previous Jinkoki, and included 12 problems at the end to challenge mathematicians in the world. ...

*Some of the terminology explanations that refer to "Cause Calculation Song" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…《塵劫記》より後に出版されたので，《塵劫記》の解説という色合いが濃いが，内容が豊富で，亀井割，弾道，月塩知死後などの問題も含まれている。本書の名前は，《塵劫記》，今村知商の《因帰算歌（いんきさんか）》(1640)，榎並和澄の《参両録》(1653)などの数学書の誤りを訂正するという意味でつけられている。《参両録》を非難するとともに，《塵劫記》の遺題を解き，さらに遺題11問を提出したことによって，遺題継承に拍車をかけた。…